Martin O'Neill's side were a little unfortunate not to take something from the match though as they dominated the first quarter of the game without ever really creating any clear-cut chances.
The first opportunity came in the 23rd minute when the impressive Lukaku drifted a weak header wide from Chris Brunt's cross but, as the game finally opened up, Black Cats striker Steven Fletcher was denied by the woodwork after Danny Graham had created the opening.
In the 29th minute, the unmarked Youssuf Mulumbu wasted a fine chance to break the deadlock, heading wide from a great position before the Baggies took the lead, Lukaku beating Simon Mignolet with his penalty after Craig Gardner was adjudged to have handled the ball.
Early in the second half, the ball sat up nicely for James Morrison on the edge of the penalty area but the midfielder fired wastefully wide before Sebastian Larsson's excellent inswinging corner found Stephane Sessegnon but he failed to get any power into his shot
Graham couldn't quite get on the end of Alfred N'Diaye's pinpoint cross before Lukaku profited from Titus Bramble's lazy back-pass by firing past Mignolet and doubling Albion's advanatge.
Sessegnon then set up a tense finish by netting with a sweet left-footed strike but, although James McClean missed a last-gasp chance to equalise, the Baggies hung on to claim their 12th win of the campaign.